A Novel Error-Correcting System Based on Product Codes for Future Magnetic Recording Channels

We propose a novel construction of product codes for high-density magnetic recording based on binary low-density parity check (LDPC) codes and binary image of Reed-Solomon (RS) codes. Moreover, two novel algorithms are proposed to decode the codes in the presence of AWGN errors and scattered hard errors (SHEs). Simulation results show that at a bit-error rate (BER) of approximately 10^-8 , our method allows improving the error performance by approximately 1.9 dB compared with that of a hard decision decoder of RS codes of the same length and code rate. For the mixed error channel, including random noise and SHEs, the signal-to-noise ratio is set at 5 dB, and 150 to 400 SHEs are randomly generated. The bit-error performance of the proposed product code shows a significant improvement over that of equivalent random LDPC codes or serial concatenation of LDPC and RS codes.